Hi, Steve. You probably could cut base molding with an vaneer saw or a cut-off disc in a Dremel tool but you would probably mess up the wall at least to some degree.
It probably is safer to remove the molding starting by cutting any paint bead with a utility knife, then getting a stiff putty knife behind the molding and finally using a pry bar. Put a shingle under your tools when prying so you don't mar the wall that way. Don't try to push the nails that held the molding back out but rather pull them all the way through the molding as that will do a lot less damage. Make your cut and replace the molding.
There will be a new board up here in a few weeks and hopefully some of the problems will be addressed.